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'''Stereology''' is the three-dimensional interpretation of two-dimensional [[cross section (geometry)|cross section]]s of materials or tissues. It provides practical techniques for extracting quantitative information about a three-dimensional material from measurements made on two-dimensional planar sections of the material. Stereology is a method that utilizes random, systematic sampling to provide unbiased and quantitative data. It is an important and efficient tool in many applications of [[microscopy]] (such as [[petrography]], [[materials science]], and biosciences including [[histology]], [[bone]] and [[neuroanatomy]]). Stereology is a developing science with many important innovations being developed mainly in Europe.{{citation needed|date=June 2020}} New innovations such as the [[proportionator]] continue to make important improvements in the efficiency of stereological procedures.▼
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▲'''Stereology''' is the three-dimensional interpretation of two-dimensional [[cross section (geometry)|cross section]]s of materials or tissues. It provides practical techniques for extracting quantitative information about a three-dimensional material from measurements made on two-dimensional planar sections of the material. Stereology is a method that utilizes random, systematic sampling to provide unbiased and quantitative data. It is an important and efficient tool in many applications of [[microscopy]] (such as [[petrography]], [[materials science]], and biosciences including [[histology]], [[bone]] and [[neuroanatomy]]). Stereology is a developing science with many important innovations being developed mainly in Europe. New innovations such as the [[proportionator]] continue to make important improvements in the efficiency of stereological procedures.
 
In addition to two-dimensional plane sections, stereology also applies to three-dimensional slabs (e.g. 3D microscope images), one-dimensional probes (e.g. needle biopsy), projected images, and other kinds of 'sampling'. It is especially useful when the sample has a lower spatial dimension than the original material.
It is especially useful when the sample has a lower spatial dimension than the original material.
Hence, stereology is often defined as the science of estimating higher-[[dimension]]al information from lower-dimensional samples.
 
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Classical applications of stereology include:
* calculating the volume fraction of quartz in a rock by measuring the area fraction of quartz on a typical polished plane section of rock ("Delesse principle" from [[Achille Delesse]]);
* calculating the surface area of pores per unit volume in a ceramic, by measuring the length of profiles of pore boundary per unit area on a typical plane section of the ceramic (multiplied by <math>4/\pi</math>);
* calculating the total length of capillaries per unit volume of a biological tissue, by counting the number of profiles of capillaries per unit area on a typical histological section of the tissue (multiplied by 2).
* Find the parameters such as Bone Volume, Trabecular thickness and trabecular number in a given sample of bone.
 
The popular science fact that the human lungs have a surface area (of gas exchange surface) equivalent to a tennis court (75 square meters), was obtained by stereological methods. Similarly for statements about the total length of nerve fibres, capillaries etc. in the human body.
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== Sampling principles ==
 
In addition to using geometrical facts, stereology applies [[statistics|statistical]] principles to extrapolate three-dimensional shapes from plane section(s) of a material.<ref>Howard, C.V., Reed, M. G. ''Unbiased Stereology (second edition)''. Garland Science/BIOS Scientific Publishers, 2005. pp.143-163 143–163</ref> The statistical principles are the same as those of [[survey sampling]] (used to draw inferences about a human population from an opinion poll, etc.).
Statisticians regard stereology as a form of sampling theory for spatial populations.
 
To extrapolate from a few plane sections to the three-dimensional material, essentially the sections must be 'typical' or 'representative' of the entire material. There are basically two ways to ensure this:
* It is assumed that any plane section is typical (e.g. assume that the material is completely homogeneous); ▼
or 'representative' of the entire material.
There are basically two ways to ensure this:
▲* It is assumed that any plane section is typical (e.g. assume that the material is completely homogeneous);
or
* Plane sections are selected at random, according to a specified random sampling protocol
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Instead of relying on model assumptions about the three-dimensional material, we take our sample of plane sections by following a randomized sampling design, for example, choosing a random position at which to start cutting the material. Extrapolation from the sample to the 3-D material is valid because of the randomness of the sampling design, so this is called ''design-based'' sampling inference.
 
Design-based stereological methods can be applied to materials which are inhomogeneous or cannot be assumed to be homogeneous. These methods have gained increasing popularity in the biomedical sciences, especially in lung-, kidney-, bone-, cancer- and neuro-science. Many of these applications are directed toward determining the number of elements in a particular structure, e.g. the total number of neurons in the brain.
These methods have gained increasing
popularity in the biomedical sciences, especially in lung-, kidney-, bone-, cancer- and neuro-science.
Many of these applications are directed toward determining the number of elements in a particular structure, e.g. the total number of neurons in the brain.
 
== Geometrical models ==
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Sampling principles also make it possible to estimate total quantities such as the total surface area of lung. Using techniques such as [[systematic sampling]] and [[cluster sampling]] we can effectively sample a fixed fraction of the entire material (without the need to delineate a reference volume). This allows us to extrapolate from the sample to the entire material, to obtain estimates of total quantities such as the absolute surface area of lung and the absolute number of cells in the brain.
 
== Stereology timelineTimeline ==
 
* 1733 [[Georges-Louis Leclerc, Comte de Buffon|G. Buffon]] discovers connections between geometry and probability, that ultimately lay the foundations for stereology.
and probability, that ultimately lay the foundations
for stereology.
 
* 1843 Mining geologist [[Achille Ernest Oscar Joseph Delesse|A. E. Delesse]] invents the first technique (Delesse's principle) for determining volume fraction in 3D from area fraction on sections.
first technique (Delesse's principle)
for determining volume fraction in 3D from area fraction on sections.
 
* 1885 mathematician [[Morgan Crofton|M.W. Crofton]] publishes theory of `geometrical probability' including stereological methods.
of `geometrical probability' including stereological methods.
 
* 1895 first known description of a correct method for counting cells in microscopy.
for counting cells in microscopy.
 
* 1898 geologist A. Rosiwal explains how to determine volume fraction from length fraction on linear transects.
volume fraction from length fraction on linear transects.
 
* 1916 S. J. Shand builds the first integrating linear accumulator to automate stereological work.
automate stereological work.
 
* 1919 committee of ASTM (American Society for Testing and Materials) established to standardise measurement of grain size.
Materials) established to standardise measurement of grain size.
 
* 1923 statistician S.D. Wicksell formulates the general problem of particle size – inferring the distribution of sizes of 3-D particles from the observed distribution of sizes of their 2-D profiles – and solves it for spherical particles.
particle size - inferring the distribution of sizes of 3-D particles
from the observed distribution of sizes of their 2-D profiles - and
solves it for spherical particles.
 
* 1929 mathematician H. Steinhaus develops stereological principles for measuring length of curves in 2D.
for measuring length of curves in 2D.
 
* 1930 geologist A.A. Glagolev builds a device for point counting with a microscope.
 
1940's* 1940s cancer researcher H. Chalkley publishes methods for determining surface area from plane sections.
determining surface area from plane sections.
 
* 1944 mathematician [[P. A. P. Moran]] describes a method for measuring the surface area of a convex object from the area of projected images.
the surface area of a convex object from the area of projected images.
 
* 1946 anatomist Abercrombie shows that many current methods for counting cells are erroneous, and proposes a correct method.
counting cells are erroneous, and proposes a correct method.
 
1946&ndash;58* 1946–58 materials scientist S.A. Saltykov publishes methods for determining surface area and length from plane sections.
determining surface area and length from plane sections.
 
* 1948 biologist H. Elias uncovers a one-hundred-year-old misunderstanding of the structure of mammalian liver.
misunderstanding of the structure of mammalian liver.
 
* 1952 Tomkeieff and Campbell calculate the internal surface area of a human lung.
of a human lung.
* 1961 word 'stereology' coined. Foundation of the International Society of Stereology
Foundation of the International Society of Stereology
 
* 1961 materials scientists Rhines and De Hoff develop a method for estimating the number of objects e.g. grains, particles, cells of convex shape.
for estimating the number of objects e.g. grains, particles, cells
of convex shape.
 
* 1966 Weibel and Elias calculate the efficiency of stereological sampling techniques.
stereological sampling techniques.
 
* 1972 E. Underwood describes stereological techniques for projected images.
projected images.
 
1975-80* 1975–80 statisticians R.E. Miles and P.J. Davy show that stereology can be formulated as a survey sampling technique, and develop design-based methods.
stereology can be formulated as a survey sampling technique,
and develop design-based methods.
 
* 1983 R.E Miles and (independently) [[Eva Vedel Jensen|E.B. Jensen]] and [[H.J.G. Gundersen]] develop ''point-sampled intercept'' methods for inferring the mean volume of arbitrarily-shaped particles from plane sections.
develop ''point-sampled intercept'' methods for inferring the
mean volume of arbitrarily-shaped particles from plane sections.
 
* 1984 D.C Sterio describes the `'disector' counting method.
counting method.
 
* 1985 stereologist H. Haug criticises the dogma that the normal human brain progressively loses neurons with age. He shows that the existing evidence is invalid.
that the normal human brain progressively loses neurons
with age. He shows that the existing evidence is invalid.
 
* 1985 statistician [[Adrian Baddeley|A. Baddeley]] introduces the method of vertical sections.
vertical sections.
 
* 1986 Gundersen proposes the `'fractionator' sampling technique.
 
1988-92* 1988–92 Gundersen and Jensen propose the `'nucleator' and 'rotator' techniques for estimating particle volume.
 
and `rotator' techniques for estimating particle volume.
* 1998 Kubinova introduces the first virtual probe that estimates surface area in preferential slices.▼
 
* 1999 Larsen and Gundersen introduce global spatial sampling for estimation of total length in preferential slices.▼
 
* 2002-04 Mouton, Gokhale, Ward and GokhaleWest introduce virtual probesprobe "space balls" (2002)for andestimation "virtualof cycloids"total (2004)length.▼
▲ 1998 Kubinova introduces the first virtual probe that estimates
surface area in preferential slices.
 
* 2004 Gokhale, Evans, Mackes and Mouton introduce virtual probe "virtual cycloids" for estimation of total surface area.
▲ 1999 Larsen and Gundersen introduce global spatial sampling
for estimation of total length in preferential slices.
 
* 2008 Gundersen, Gardi, Nyengaard introduce the [[proportionator]] method.▼
▲ 2002-04 Mouton and Gokhale introduce virtual probes "space balls" (2002) and "virtual cycloids" (2004)
for estimation of total length and total surface area, respectively, in arbitrary slices.
 
The primary scientific journals for stereology are "Journal of Microscopy" and "''[[Image Analysis & Stereology"]]'' (exformer ''Acta Stereologica''). and ''Journal of Microscopy'' ▼
▲ 2008 Gundersen, Gardi, Nyengaard introduce the [[proportionator]]
the most efficient stereological method known.
 
== See also ==
▲The primary scientific journals for stereology are "Journal of Microscopy" and "Image Analysis & Stereology" (ex Acta Stereologica).
 
* [[Merz grid]]
== References ==
{{Reflist}}
* Baddeley, A., and [[Eva Vedel Jensen|E. B. Vedel Jensen]] (2005), Stereology For Statisticians, Chapman & Hall/CRC. {{ISBN |9781584884057}}
* Evans, S.M., Janson, A.M., Nyengaard, J.R. (2004).Quantitative Methods in Neuroscience: A Neuroanatomical Approach. Oxford University Press, USA. {{ISBN |978-0198505280}}▼
* Mouton, Peter R. (2002). Principles and Practices of Unbiased Stereology: An Introduction For Bioscientists. Baltimore: Johns Hopkins University Press. ISBN 0-8018-6797-5. ▼
* [[Eva Vedel Jensen|Vedel Jensen Eva B.V.]] (1998) Local Stereology. Advanced Series on Statistical Science & Applied Probability Vol. 5. World Scientific Publishing. {{ISBN |981-02-2454-0}}▼
* P.R. Mouton (2011). Unbiased Stereology: A Concise Guide. The Johns Hopkins University Press, Baltimore, MD. ISBN 978-0-8018-9984-3
▲* Mouton, Peter R. (2002). Principles and Practices of Unbiased Stereology: An Introduction For Bioscientists. Baltimore: Johns Hopkins University Press. {{ISBN |0-8018-6797-5}}.
* Mouton, P.R. "Neurostereology" (2014) Wiley-Blackwell Press, Boston, MA. {{ISBN |1118444213}}.
▲* Evans, S.M., Janson, A.M., Nyengaard, J.R. (2004).Quantitative Methods in Neuroscience: A Neuroanatomical Approach. Oxford University Press, USA. ISBN 978-0198505280
* West,P.R. Mark J.Mouton (20122011). BasicUnbiased Stereology: -A ForConcise BiologistsGuide. andThe Neuroscientists.Johns ColdHopkins SpringUniversity HarborPress, LaboratoryBaltimore, PressMD. {{ISBN |978-10-9361138018-609984-63}}
* Schmitz, C., and P. R. Hof. "Design-based stereology in neuroscience." Neuroscience 130, no. 4 (2005): 813–831.
▲* Jensen Eva B.V. (1998) Local Stereology. Advanced Series on Statistical Science & Applied Probability Vol. 5. World Scientific Publishing. ISBN 981-02-2454-0
* West, Mark J. (2012). Basic Stereology – For Biologists and Neuroscientists. Cold Spring Harbor Laboratory Press. {{ISBN|978-1-936113-60-6}}
* West, M.J., L. Slomianka, and H.J.G. Gundersen : Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the Optical Fractionator. Anatomical Record 231: 482–497, 1991.
 
== External links ==
*[http://www.stereologysociety.org/ International Society for Stereology]
*[httphttps://www.wiseias-tiss.comorg/iasojs/IAS/ Image Analysis & Stereology]
*[http://www.stereology.info/ Stereology Info]
*[http://www.stereothenainc.com/ Stereothena]
 
[[Category:Microscopy]]
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